Nonlinear feedback, double bracket dissipation and port control of Lie-Poisson systems

Methods from controlled Lagrangians, double bracket dissipation and interconnection and damping assignment -- passivity based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie-Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow

Differentiation and Passivity for Control of Brayton-Moser Systems

This paper deals with a class of Resistive-Inductive-Capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in Brayton Moser framework. For this class of systems, new passivity properties using a Krasovskii's type Lyapunov function as storage function are presented. Consequently, the supply-rate is a function of the system states, inputs and their first time-derivatives. Moreover, after showing the integrability property of the port-variables, two simple control methodologies called output shaping and input shaping are proposed for regulating the voltage in RLC and s-RLC circuits. Global asymptotic convergence to the desired operating point is theoretically proved for both proposed control methodologies. Moreover, robustness with respect to load uncertainty is ensured by the input shaping methodology. The applicability of the proposed methodologies is illustrated by designing voltage controllers for DC-DC converters and DC networks

A constructive procedure for energy shaping of port-Hamiltonian systems

International audienceEquilibrium stabilization of nonlinear systems via energy shaping is a well-established, robust, passivity-based controller design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations, which is usually a difficult task. In this paper a new, fully constructive, procedure to shape the energy for a class of port-Hamiltonian systems that obviates the solution of partial differential equations is proposed. Proceeding from the well-known passive, power shaping output we propose a nonlinear static state-feedback that preserves passivity of this output but with a new storage function. A suitable selection of a controller gain makes this function positive definite, hence it is a suitable Lyapunov function for the closed-loop. The resulting controller may be interpreted as a classical PI—connections with other standard passivity-based controllers are also identified